<html lang="en">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<title>reference</title>
<style type="text/css">
	body {background-color: white; color: black; font-family:sans-serif; font-size:medium;}
	a:link {color: #3300ff;}
	a:visited {color: #663399;}
	a:hover {color:#0099ff;}
	a:active {color: #0066cc;}
	a.button {text-decoration:none;}
	
	table.nav  {background-color: #dbddff;}
	table.body {margin-top:2ex; margin-bottom:2ex;}
	table.programlistingindent {margin-left:32px;}
	
	img { margin-bottom:0px; margin-top:0px;}
	tt {margin-left:0.5em; margin-right:0.5em; font-weight:lighter;}
	
	p {margin-top:0ex;}
	p.synopsis {margin-left:32px;}
	p.programlistingindent {margin-left:32px;}
	p.citetitle {margin-left:2em;}
	
	ul ul {list-style-type:square;}
	ul li p {margin-top:0ex; margin-bottom:.5ex; padding:0}
	ol li p {margin-top:0ex; margin-bottom:.5ex; padding:0}
	
	h1.reftitle {color:#a90000;}
	h1.reftitle {font-size:3.7ex; margin-top:0; margin-bottom:0; font-weight:bold}
	h1.title {color:black; font-size:4ex; margin-top:1ex; font-weight:bold}
	h2.title {color:#bd0000; margin-top:1ex; margin-bottom:.9ex; font-weight:bold; font-size:3ex}
	h3.title {color:#bd0000; margin-top:1ex; margin-bottom:.9ex; font-weight:bold; font-size:2.5ex}
	h4.title {color:#bd0000; margin-top:1ex; margin-bottom:.9ex; font-weight:bold; font-size:2ex}
	h2 {color:#bd0000; margin-top:1ex; margin-bottom:.9ex; font-weight:bold; font-size:2.5ex}
	h3 {color:#bd0000; margin-top:1ex; margin-bottom:.9ex; font-weight:bold; font-size:2ex} 
	
	pre.programlisting {margin-left:32px;}
	pre.synopsis {margin-left:32px;}
	
	
	.categorytitle {margin-top:8px; padding-top:0px;}
	.categorylist {background-color: #e1e6f2;}
 	</style>
</head>
<body>
<a name="top_of_page"></a><p style="font-size:1px;"></p>
<h1 class="reftitle">reference</h1>
<h2>Purpose</h2>
<p>Penalizes difference of a signal from a given reference level</p>
<h2>Syntax</h2>
<pre class="synopsis"></pre>
<h2>Description</h2>
<p></p> 
    Adding this filter to an MPC setup will modify the objective
    function in such a way that the difference between actual signal
    and a prescribed reference signal is minimized.<br><br>

    To enable this filter, call <tt>model.x.with('reference')</tt>,
    which will enable tracking of state references by minimizing <img src="../../../../../fig/mpt/modules/ui/@SystemSignal/filter_reference1.png" alt="../../../../../fig/mpt/modules/ui/@SystemSignal/filter_reference1.png">. You can also add tracking to input and/or
    output signals by using <tt>model.u.with('reference')</tt> and
    <tt>model.y.with('reference')</tt>, respectively.<br><br>

    Once the filter is enabled, the reference trajectory can be
    specified in the signal's <tt>reference</tt> property:<br><br>

    
      <tt>model.x.reference = [0.5; -1]</tt>
      <br><br>

    The reference signal can also be time-varying. In such a case the
    <img src="../../../../../fig/mpt/modules/ui/@SystemSignal/filter_reference2.png" alt="../../../../../fig/mpt/modules/ui/@SystemSignal/filter_reference2.png">-th column of the reference is interpreted as the
    reference to be used at the <img src="../../../../../fig/mpt/modules/ui/@SystemSignal/filter_reference3.png" alt="../../../../../fig/mpt/modules/ui/@SystemSignal/filter_reference3.png">-th step of the prediction:<br><br>

    
      <tt>model.u.reference = [-1 -2 0 0 1]</tt>
      <br><br>

    The filter can be removed by calling
    <tt>model.x.without('reference')</tt>. 

  <h2>Example(s)</h2>
<h3>Example 
				1</h3>Create a 1D LTI system <img src="../../../../../fig/mpt/modules/ui/@SystemSignal/filter_reference4.png" alt="../../../../../fig/mpt/modules/ui/@SystemSignal/filter_reference4.png">.<pre class="programlisting">model = LTISystem('A', 0.9, 'B', 1);</pre>
<pre class="programlisting"></pre>Enable tracking of state and input references.<pre class="programlisting">
		model.x.with('reference'); 
		model.u.with('reference');
		model.x.reference = 0.4;
		model.u.reference = 1;
		model.x.penalty = QuadFunction(1);
		model.u.penalty = QuadFunction(1);
	</pre>
<pre class="programlisting"></pre>
<p></p>
<table class="nav" summary="Navigation aid" border="0" width="100%" cellpadding="0" cellspacing="0"><tr valign="top">
<td align="left" width="20">
<a href="filter_setconstraint.html" class="button">&#9664;</a>  </td>
<td align="left">filter_setconstraint</td>
<td>  </td>
<td align="right">mpt</td>
<td align="right" width="20"><a href="../../../../mpt.html" class="button">&#9654;</a></td>
</tr></table>
<br><p>©  <b>2003-2013</b>     Michal Kvasnica: STU Bratislava,    <a href="mailto:michal.kvasnica@stuba.sk">michal.kvasnica@stuba.sk</a></p>
</body>
</html>
